Finite Group Databasebeta

← #8126979

Subgroups — #8126979

Order 512.

4810 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59369C212yesmaximal, complemented
2#59189C212yesmaximal, complemented
3#58837C214yesmaximal, complemented
4#56477C214yesmaximal, complemented
5#54629C214yesmaximal, complemented
6#54125C214yesmaximal, complemented
7#51323C214yesmaximal, complemented
8#50446C214yesmaximal, complemented
9#50400C214yesmaximal, complemented
10#50225C214yesmaximal, complemented
11#45539C212yesmaximal, complemented
12#45537C212yesmaximal, complemented
13#40837C214yesmaximal, complemented
14#40811C214yesmaximal, complemented
15#39512C212yesmaximal, complemented
16#39499C212yesmaximal, complemented
17#39422C212yesmaximal, complemented
18#39413C212yesmaximal, complemented
19#36720C211yesmaximal, characteristic, complemented
20#36710C211yesmaximal, characteristic
21#35260C212yesmaximal, complemented
22#34989C212yesmaximal, complemented
23C2×#2413C211yesmaximal, characteristic, complemented
24C2×#559C2212yes—
25C2×#543C2211yescharacteristic
26C2×#542C2212yescomplemented
27C2×#539C2212yes—
28C2×#537C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2857C2212yes—
34#2850C2212yes—
35#2849C2214yes—
36#2848C2212yes—
37#2847C2212yes—
38#2839C2214yescomplemented
39#2837C2214yescomplemented
40#2835C2212yescomplemented
41#2831C2214yescomplemented
42#2826C2214yes—
43#2826C2214yescomplemented
44#2824C2212yescomplemented
45#2810C2214yescomplemented
46#2805C2214yescomplemented
47#2804C2214yescomplemented
48#2803C2214yescomplemented
49#2799C2214yescomplemented
50#2795C2214yescomplemented
51#2790C2214yescomplemented
52#2788C2214yescomplemented
53#2783C2214yescomplemented
54#2782C2214yescomplemented
55#2782C2214yescomplemented
56#2780C2214yescomplemented
57#2778C2214yes—
58#2778C2214yes—
59#2776C2214yescomplemented
60#2776C2214yescomplemented
61#2775C2214yescomplemented
62#2770C2214yescomplemented
63#2766C2214yescomplemented
64#2764C2212yescomplemented
65#2763C2212yescomplemented
66#2763C2214yescomplemented
67#2761C2214yescomplemented
68#2760C2212yescomplemented
69#2757C2214yes—
70#2754C2214yescomplemented
71#2753C2214yescomplemented
72#2749C2214yescomplemented
73#2748C2212yes—
74#2743C2214yescomplemented
75#2743C2214yescomplemented
76#2738C2214yescomplemented
77#2731C2214yescomplemented
78#2730C2214yescomplemented
79#2728C2214yescomplemented
80#2724C2212yes—
81#2718C2214yescomplemented
82#2715C2214yescomplemented
83#2712C2212yescomplemented
84#2710C2214yes—
85#2709C2212yes—
86#2709C2214yes—
87#2709C2212yes—
88#2704C2214yescomplemented
89#2702C2214yescomplemented
90#2701C2214yescomplemented
91#2698C2214yescomplemented
92#2696C2214yes—
93#2696C2214yes—
94#2696C2214yescomplemented
95#2693C2214yes—
96#2690C2214yescomplemented
97#2687C2214yes—
98#2687C2214yes—
99#2687C2214yescomplemented
100#2680C2214yes—
101#2680C2214yes—
102#2673C2214yes—
103#2673C2214yes—
104#2672C2214yescomplemented
105#2665C2214yescomplemented
106#2654C2214yescomplemented
107#2653C2214yescomplemented
108#2649C2214yescomplemented
109#2647C2214yescomplemented
110#2643C2214yescomplemented
111#2637C2214yescomplemented
112#2636C2214yescomplemented
113#2628C2212yescomplemented
114#2627C2212yes—
115#2627C2212yes—
116#2625C2212yescomplemented
117#2624C2212yescomplemented
118#2623C2214yes—
119#2620C2212yescomplemented
120#2618C2212yes—
121#2617C2212yes—
122#2607C2212yescomplemented
123#2602C2214yes—
124#2600C2212yescomplemented
125#2591C2212yes—
126#2581C2214yescomplemented
127#2576C2214yescomplemented
128#2572C2214yescomplemented
129#2570C2214yescomplemented
130#2561C2212yes—
131#2560C2214yescomplemented
132#2559C2214yescomplemented
133#2557C2214yes—
134#2556C2214yescomplemented
135#2549C2214yescomplemented
136#2536C2214yescomplemented
137#2534C2214yes—
138#2532C2214yescomplemented
139#2532C2214yescomplemented
140#2527C2214yescomplemented
141#2526C2214yescomplemented
142#2518C2214yescomplemented
143#2514C2214yescomplemented
144#2503C2214yes—
145#2502C2212yes—
146#2493C2214yes—
147#2493C2214yes—
148#2489C2214yescomplemented
149#2488C2214yes—
150#2488C2214yes—
151#2483C2212yes—
152#2481C2214yes—
153#2481C2214yescomplemented
154#2481C2214yescomplemented
155#2479C2214yescomplemented
156#2477C2214yescomplemented
157#2474C2214yescomplemented
158#2473C2214yescomplemented
159#2473C2214yescomplemented
160#2472C2214yes—
161#2472C2214yes—
162#2470C2214yescomplemented
163#2461C2214yescomplemented
164#2459C2214yescomplemented
165#2458C2214yes—
166#2457C2214yescomplemented
167#2455C2214yes—
168#2450C2214yes—
169#2450C2214yescomplemented
170#2449C2214yes—
171#2449C2214yescomplemented
172#2449C2214yescomplemented
173#2446C2214yescomplemented
174#2445C2214yes—
175#2443C2214yes—
176#2443C2214yescomplemented
177#2443C2214yescomplemented
178#2433C2212yes—
179#2425C2214yes—
180#2425C2214yescomplemented
181#2423C2214yescomplemented
182#2419C2214yescomplemented
183#2418C2214yes—
184#2413C2214yes—
185#2413C2214yes—
186#2413C2214yes—
187#2413C2214yes—
188#2412C2214yes—
189#2406C2214yes—
190#2405C2212yes—
191#2404C2212yes—
192#2404C2212yes—
193C2×#398C2212yes—
194C2×#396C2212yes—
195#2380C2212yes—
196#2379C2214yescomplemented
197#2376C2212yes—
198#2374C2212yes—
199#2360C2214yes—
200#2358C2214yes—
201#2353C2214yes—
202#2353C2214yescomplemented
203#2339C2214yes—
204#2324C2212yescomplemented
205#2323C2212yescomplemented
206#2322C2214yes—
207#2314C2212yescomplemented
208#2313C2212yes—
209#2313C2211yescharacteristic
210#2312C2211yescharacteristic
211C4×C22⋊Q8C2212yes—
212C4×#121C2212yes—
213C4×#120C2214yes—
214C2×#389C2212yes—
215C2×#388C2212yes—
216C2×#386C2211yescharacteristic
217C2×#385C2211yescharacteristic
218C2×#381C2211yescharacteristic
219C22×#41C2312yes—
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#559—48no—
225#543—44no—
226#542—48no—
227#539—48no—
228#537—44no—
229C2×C4⋊Q8C2312yes—
230C2×#127C2312yes—
231C2×#127C2312yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#125C2314yes—
235C2×#124C2314yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#123—44no—
239C2×#123—44no—
240C2×#123C2312yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2312yes—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#120C2314yes—
268C2×#120C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×#117—44no—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C22×C4⋊C4—44no—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2314yes—
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C42C2312yes—
301#401C2314yes—
302#401C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2312yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2312yes—
403#393C2312yes—
404#393C2314yes—
405#393C2314yes—
406#393C2312yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#392C2312yes—
412#392C2314yes—
413#392C2314yes—
414#392C2312yes—
415#392C2314yes—
416#392C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#390C2314yes—
430#390C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2312yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2312yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#384C2312yes—
570#384C2314yes—
571#383C2314yes—
572#383C2314yes—
573#383C2314yes—
574#382C2312yes—
575#382C2314yes—
576#382C2314yes—
577#382C2314yes—
578#382C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2312yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#381C2314yes—
588#381C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#379C2314yes—
602#379C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2314yes—
618C2×#95C2312yes—
619C2×#95C2314yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C2×#41—44no—
626C2×#41—48no—
627C22×Q8C2412yes—
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×D4—42no—
632C22×D4—42no—
633C22×D4—42no—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C23×C4—24no—
645C23×C4—42no—
646C23×C4—42no—
647C23×C4—44no—
648C23×C4—42no—
649C23×C4—42no—
650C23×C4—42no—
651C23×C4—42no—
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C4⋊Q8—44no—
673#127—44no—
674#127—44no—
675#126—48no—
676#126—48no—
677#125—48no—
678#124—216no—
679#124—44no—
680#124—48no—
681#123—28no—
682#123—48no—
683#123—48no—
684#123—44no—
685#123—48no—
686#123—44no—
687#123—48no—
688#123—48no—
689#123—44no—
690#123—48no—
691#123—48no—
692#123—48no—
693C22⋊Q8—28no—
694C22⋊Q8—44no—
695C22⋊Q8—48no—
696C22⋊Q8—44no—
697C22⋊Q8—44no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702C22⋊Q8—48no—
703#121—28no—
704#121—48no—
705#121—44no—
706#121—44no—
707#121—44no—
708#120—48no—
709#120—48no—
710C4×Q8—44no—
711C4×Q8—48no—
712C4×D4—44no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—48no—
718#117—28no—
719#117—44no—
720#117—44no—
721#117—44no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—24no—
724C2×C4⋊C4—48no—
725C2×C4⋊C4—48no—
726C2×C4⋊C4—44no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—44no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—42no—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C22⋊C4—24no—
775C2×C22⋊C4—24no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—42no—
778C2×C22⋊C4—44no—
779C2×C22⋊C4—44no—
780C2×C22⋊C4—42no—
781C2×C22⋊C4—42no—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2411yescharacteristic
831C2×C42—44no—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899C24—22no—
900C24—22no—
901C24—22no—
902C24—24no—
903C24—22no—
904C24—24no—
905C24—42no—
906C24—41no—
907C24—41no—
908C24—42no—
909C24C2512yes—
910C24C2514yes—
911C24C2511yescharacteristic
912C24C2511yescharacteristic
913C24C2511yescharacteristic
914#41—816no—
915C2×Q8—28no—
916C2×Q8—24no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×Q8—42no—
921C2×Q8—44no—
922C2×Q8—44no—
923C2×Q8—42no—
924C2×Q8—44no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—88no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—22no—
965C22×C4—24no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—41no—
979C22×C4—42no—
980C22×C4—41no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—41no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—41no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—416no—
1010C22×C4—416no—
1011C22×C4—88no—
1012C22×C4H(5,𝔽2)14yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C22⋊C4—22no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4H(5,𝔽2)14yes—
1123C42—24no—
1124C42—24no—
1125C42—28no—
1126C42—42no—
1127C42—42no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—42no—
1135C42—42no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—28no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—24no—
1150C23—22no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—48no—
1161C23—48no—
1162C23—44no—
1163C23—44no—
1164C23—44no—
1165C23—82no—
1166C23—82no—
1167C23—84no—
1168C23—84no—
1169C23C2×H(5,𝔽2)12yes—
1170C23C2×H(5,𝔽2)12yes—
1171C23#58512yes—
1172C23#58514yes—
1173C23C2611yescharacteristic
1174Q8—84no—
1175Q8—88no—
1176Q8—84no—
1177Q8—162no—
1178D4—416no—
1179D4—84no—
1180D4—88no—
1181D4—88no—
1182D4—84no—
1183D4—84no—
1184D4—88no—
1185D4—84no—
1186D4—162no—
1187D4—164no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—44no—
1239C2×C4—48no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—44no—
1243C2×C4—48no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—44no—
1247C2×C4—82no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—82no—
1253C2×C4—88no—
1254C2×C4—164no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—164no—
1258C2×C4C2×H(5,𝔽2)14yes—
1259C2×C4C2×H(5,𝔽2)14yes—
1260C22—22no—
1261C22—22no—
1262C22—24no—
1263C22—24no—
1264C22—22no—
1265C22—22no—
1266C22—24no—
1267C22—24no—
1268C22—416no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—164no—
1288C22#354014yes—
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×H(5,𝔽2)11yescharacteristic
1291C22C2×#58512yes—
1292C22C2×#58511yescharacteristic
1293C222−1+612yes—
1294C4—24no—
1295C4—24no—
1296C4—44no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—44no—
1303C4—42no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C4—44no—
1312C2—24no—
1313C2—42no—
1314C2—42no—
1315C2—84no—
1316C2—82no—
1317C2C2×#354011yescharacteristic
1318C2#6281811yescharacteristic
1319C2#6288711yescharacteristic
1320C2#6289812yes—
1321C2#6290912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36710C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59369C2semidirect
2. #59189C2semidirect
3. #58837C2semidirect
4. #56477C2semidirect
5. #54629C2semidirect
6. #54125C2semidirect
7. #51323C2semidirect
8. #50446C2semidirect
9. #50400C2semidirect
10. #50225C2semidirect
11. #45539C2semidirect
12. #45537C2semidirect
13. #40837C2semidirect
14. #40811C2semidirect
15. #39512C2semidirect
16. #39499C2semidirect
17. #39422C2semidirect
18. #39413C2semidirect
19. #36720C2semidirect
21. #35260C2semidirect
22. #34989C2semidirect
23. C2×#2413C2semidirect
26. C2×#542C22semidirect
38. #2839C22semidirect
39. #2837C22semidirect
40. #2835C22semidirect
41. #2831C22semidirect
43. #2826C22semidirect
44. #2824C22semidirect
45. #2810C22semidirect
46. #2805C22semidirect
47. #2804C22semidirect
48. #2803C22semidirect
49. #2799C22semidirect
50. #2795C22semidirect
51. #2790C22semidirect
52. #2788C22semidirect
53. #2783C22semidirect
54. #2782C22semidirect
55. #2782C22semidirect
56. #2780C22semidirect
59. #2776C22semidirect
60. #2776C22semidirect
61. #2775C22semidirect
62. #2770C22semidirect
63. #2766C22semidirect
64. #2764C22semidirect
65. #2763C22semidirect
66. #2763C22semidirect
67. #2761C22semidirect
68. #2760C22semidirect
70. #2754C22semidirect
71. #2753C22semidirect
72. #2749C22semidirect
74. #2743C22semidirect
75. #2743C22semidirect
76. #2738C22semidirect
77. #2731C22semidirect
78. #2730C22semidirect
79. #2728C22semidirect
81. #2718C22semidirect
82. #2715C22semidirect
83. #2712C22semidirect
88. #2704C22semidirect
89. #2702C22semidirect
90. #2701C22semidirect
91. #2698C22semidirect
94. #2696C22semidirect
96. #2690C22semidirect
99. #2687C22semidirect
104. #2672C22semidirect
105. #2665C22semidirect
106. #2654C22semidirect
107. #2653C22semidirect
108. #2649C22semidirect
109. #2647C22semidirect
110. #2643C22semidirect
111. #2637C22semidirect
112. #2636C22semidirect
113. #2628C22semidirect
116. #2625C22semidirect
117. #2624C22semidirect
119. #2620C22semidirect
122. #2607C22semidirect
124. #2600C22semidirect
126. #2581C22semidirect
127. #2576C22semidirect
128. #2572C22semidirect
129. #2570C22semidirect
131. #2560C22semidirect
132. #2559C22semidirect
134. #2556C22semidirect
135. #2549C22semidirect
136. #2536C22semidirect
138. #2532C22semidirect
139. #2532C22semidirect
140. #2527C22semidirect
141. #2526C22semidirect
142. #2518C22semidirect
143. #2514C22semidirect
148. #2489C22semidirect
153. #2481C22semidirect
154. #2481C22semidirect
155. #2479C22semidirect
156. #2477C22semidirect
157. #2474C22semidirect
158. #2473C22semidirect
159. #2473C22semidirect
162. #2470C22semidirect
163. #2461C22semidirect
164. #2459C22semidirect
166. #2457C22semidirect
169. #2450C22semidirect
171. #2449C22semidirect
172. #2449C22semidirect
173. #2446C22semidirect
176. #2443C22semidirect
177. #2443C22semidirect
180. #2425C22semidirect
181. #2423C22semidirect
182. #2419C22semidirect
196. #2379C22semidirect
202. #2353C22semidirect
204. #2324C22semidirect
205. #2323C22semidirect
207. #2314C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#593692
#591892
#588372
#564772
#546292
#541252
#513232
#504462
#504002
#502252
#455392
#455372
#408372
#408112
#395122
#394992
#394222
#394132
#367202
#367102
#352602
#349892
C2×#24132